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If n^(th) division of main scale coincid...

If `n^(th)` division of main scale coincides with `(n + 1)^(th)` divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.

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`(N +1)` divisions on the vernier scale `= N` divisions on main scale
`:.` 1 division on virnier scale `=N/(N +1)` divisions on main scale
Each division on the main scale is of a units.
`:.` 1 division on verneir scale `= (N/(N +1))` a units = a' (say)
Least count = 1 main scale division - 1 vernier scale division
`=a -a' =a-((N)/(N+ 1))a = a/(N +1)`.
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